I pre-ordered it so I would get Nuketown 2025 and get double exp as well, When I kill someone or do the objective it will show me +100 on TDM or +50 on random game mode.It doesn't seem like I'm getting the double exp

The little number that appears in the center of the screen when you kill someone or capture an objective is the "score" you earned for doing so. That's what helps you unlock your streaks, such as the UAV, Hunter Killer, etc.

Previous games in the Call of Duty series would be showing double what you normally get upon accomplishing something, but that's because they were showing the amount of XP you earned for doing so. Now, if you look at the after-action report in the lobby during intermission (back on the Xbox, select on the PS3) you can see the lighter part of the XP bar, and compared to normal XP, it is much larger.

To my knowledge, there is no way to tell how much experience you are earning each game, but it seems to be quite a bit. You can see the exact number for your Match Bonus at the end of each match, before the final killcam, but besides that I do not believe there is a way to check.

Edit: If you have an account with Call of Duty Elite (which is completely free, and useful), you can see your experience if you go under:Browse > Black Ops II > Career